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  • 1
    Electronic Resource
    Electronic Resource
    Instability in degenerate two-photon running wave laser with detuning (1988)
    Springer
    The European physical journal 71 (1988), S. 247-252 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The previous stability analysis of the degenerate two-photon running wave laser is extended to the inclusion of detuning between frequencies of cavity and atoms. We derive the analytical equation for the critical pumping and prove analytically that for the special case ofr (γ∥/γ⊥) being unity, there is no Hopf bifurcation instability for the bad cavity. The good cavity case is analysed numerically. The role played by detuning is to raise the critical pumping. In the case ofk〈r (or 〈Kγ∥) where there is no Hopf bifurcation instability for the perfect tuning case, the large detuning can give rise to self-pulsing instability.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01312796
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    Paper (German National Licenses)
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  • 2
    Electronic Resource
    Electronic Resource
    Quasiperiodicity involving twin oscillations in the complex Lorenz equations describing a detuned laser (1990)
    Springer
    The European physical journal 81 (1990), S. 457-461 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Quasiperiodical motion in the complex Lorenz equations describing a detuned laser is shown to consist of twin oscillations: the first oscillation originates from Hopf bifurcation and the second is a parastic oscillation of the first one. Equations for the twin asymptotic oscillations are analytically derived in the center manifold, showing explicitly the parastic property of the second oscillation: its frequency is proportional to the square of the amplitude of the first one. The phase of the second oscillation shows also certainanholonomy which is very similar to the characteristics of Berry's phase. Numerical results show further that the first oscillation follows the sequence of bifurcations from simple periodic through period-doubling to chaos, as one continuously increases the control parameter, whereas the frequency of the parastic oscillation does not change qualitatively during the bifurcation process.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01390829
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    Paper (German National Licenses)
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  • 3
    Electronic Resource
    Electronic Resource
    Generalized Ginzburg-Landau equation for self-pulsing instability in a two-photon laser (1989)
    Springer
    The European physical journal 77 (1989), S. 163-174 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract A nonlinear analysis is made for a degenerate two-photon ring laser near its critical point corresponding to a self-pulsing instability by using the slaving principle and normal form theory. It turns out that the system undergoes two kinds of transitions, a usual Hopf bifurcation to a stable or unstable limit cycle and a co-dimension two Hopf bifurcation where the limit cycles disappear. An analytical criterion is given to distinguish the super-from the sub-critical bifurcation. We have also solved the equations numerically to confirm and to supplement our analytical results. In the case of super-critical bifurcation, a period-doubling bifurcation sequence to chaos is also observed with the decrease in pumping.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313634
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  • 4
    Electronic Resource
    Electronic Resource
    Instability in degenerate two-photon running wave laser (1989)
    Springer
    The European physical journal 77 (1989), S. 157-162 
    Details
    ISSN: 1434-6036
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract The stability of the homogeneously broadened and degenerate two-photon running wave laser is analysed by using the full set of matter-field equations. The stability depends on the relative size of the relaxation constants. For 2k〉1+r(k=κ/γ⊥,r=γ∥/γ⊥; κ is the cavity loss of the field and γ∥,γ⊥ are the longitudinal and transversal decay constants, respectively) no stable lasing state exists. Forr〈k〈(1+r)/2 an instability occurs. With the decrease in pumping the stable lasing state loses its stability due to Hopf-bifurcation.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01313633
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    Paper (German National Licenses)
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